A power transmission device is known that includes a damper absorbing torsional vibration between a fluid transmission device with a lockup clutch and an engine. Such a power transmission device is referred to as of a pre-damper type in contrast to the case that a damper is disposed in series with the lockup clutch within the fluid transmission device. Devices described in Patent Documents 1 and 2 are examples thereof and a torque converter is used as the fluid transmission device. When the engine is started in such a power transmission device, engine start control such as cranking, fuel injection, and ignition is generally provided while the lockup clutch is released.